Stability approaches for Takagi-Sugeno systems

This work concerns different stability approaches for Takagi-Sugeno (T-S) fuzzy systems. We present some recent approaches based on the idea of multiple Lyapunov functions and slack matrices to reduce the conservatism of stability analysis conditions. Then, new stability conditions are proposed in order to more reduce the conservatism using another upper bound of time-derivative of membership functions, fuzzy Lyapunov functions and slack matrices. Consequently, a large stability domain is obtained. Finally, examples are provided to illustrate the effectiveness of the proposed approaches in stability analysis